My question is about Set and Relation Theory.
$R$ is a relation on a set $S$.
1) Show that if $R^2 = R$ then $R$ is transitive.
2) Show that if $R$ is transitive and "Reflexive or Symmetric" Then $R=R^2$. (It means that for a transitive and reflexive relation we have $R = R^2$ and for a transitive and Symmetric relation we have $R=R^2$)
For 1, My proof is: Let $aRb$ and $bRc$ then by definition of R^2 we have $a R^2 b$ and because $R^2 = R$, we have $a R c$. so $R$ is transitive.
But I don't know what to do for 2.
Is my answer to "1)" correct? How to approach 2?